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Pattern formation

Instability of new type driven by ponderomotive forces of the self-magnetic field of the magnetic liquid was discovered in 1980. Magnetic liquid in the Hele-Shaw cell under the action of the perpendicular field forms labyrinthine structures. This is an unique example of the labyrinthine pattern formation inthe condition of conserved order parameter. The different instability thresholds leading to labyrinthine pattern formation were calculated. The Dynamics of the pattern formation is described in the Hele-Shaw approximation including ponderomotive forces of the self-magnetic field. The renormalization of the effective surface tension due to the magnetodipolar interactions was considered and different undulation instabilities analyzed - Chevron formation in the periodic system of magnetic liquid stripes, the bending of the Plateau borders in the magnetic foam. The numerical codes for the simulation of the pattern formation based on the boundary integral equation technique were developed. By it figures of equilibrium of the magnetic liquid drops due to the capillary and magnetic forces were found. The formation of the Steiner trees during the development of the instabilities were demonstrated. Later the pattern formation at the Interface of miscible magnetic and non-magnetic fluids - so-called magnetic microconvection was studied. The thresholds for development of microconvection were calculated and results of its numerical simulations compared with experiment.

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  30. A.Tatulchenkov, and A.Cēbers. Magnetic fluid labyrinthine instability in Hele-Shaw cell with time dependent gap. Physics of Fluids – 2008, v.20, 054101. 
  31. I.Driķis, and A.Cēbers. Pattern formation at magnetophoretical motion in the self-magnetic field of magnetic colloid. Magnetohydrodynamics – 2011, v.47, 3-10. 
  32. K.Ērglis, A.Tatulcenkov, G.Kitenbergs, O.Petrichenko, F.G.Ergin, B.B.Watz and A.Cēbers. Magnetic field driven micro-convection in the Hele-Shaw cell. J.Fluid Mech. -2013,v.714,P.612-633. 
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